Tumors typically evolve from a single (or group of) cancerous cell(s) and grow multiplicatively via cross-talk with other nearby cells, thereby producing a central necrosis region (dead cells) [1]}. Hence, as we move from the inner core of a tumor toward the exterior, different layers of the tumor possess distinct tissue characteristics. Therefore, it is important to construct imaging phenotypes which (a) mimic the underlying tumor evolution process, and (b) efficiently harness the tumor heterogeneity from the imaging scans, for downstream modeling and interpretations. To address (a), we divide the tumor region into one inner sphere followed by concentric spherical shells which potentially capture the tumor growth process. In Figure REF , we show a visualization of an example tumor region divided into three spherical layers. Tumor spheroids (cell cultures with necrotic core and peripheral layer of proliferative cells) have been used as reliable models of in vitro solid tumors [2]}, [3]}. To address (b), we propose to work with the probability density functions (smoothed histograms) constructed using layer-wise tumor voxel intensities from three-dimensional (3D) MRI scans. These probability density functions (PDFs) are the data objects of interest and capture the entire information about the distribution of voxel intensities, no longer requiring any summaries of the distribution. Recent studies have successfully utilized density-based approaches in unsupervised clustering [4]} and regression models for radiogenomic analyses [5]}, [6]}.
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